Implementation of the Cyclic Cluster Model in Hartree-Fock LCAO Calculations of Crystalline Systems

Abstract

The cyclic cluster model combines advantages of periodic and molecular cluster models for the quantum chemical treatment of perfect and defective crystalline solids. Implementations of this model into molecular codes have so far been realized for semiempirical and local density functional methods only. Due to the occurrence of four-center integrals in ab initio Hartree-Fock methods, the cyclic cluster model is difficult to realize for this case. This study presents a simple procedure for the extraction of cyclic cluster models from periodic Hartree-Fock calculations, based on the idempotency relations of the density matrix. The dependence of calculated results for bulk properties of defect-free titanium dioxide (rutile) from the size and shape of the cyclic clusters is investigated. It is demonstrated that by a proper choice of cyclic clusters where full spheres of nearest neighbor atoms are taken into account, relatively small cyclic clusters can reproduce results for total energies and one-electron energies obtained with full band structure calculations.